Sure! IT people do it all the time!
If you can get ahold of a CD, simply copy the contents of the i386 folder to an already-formatted FAT32 hard drive. Then, you can boot to a floppy to begin the installation. You can run the command x:\i386\winnt32.exe to begin the Windows installation, where X: is the letter of the drive the i386 folder is stored on when you're booted to the DOS disk.
Keep in mind, though, that you will still need a valid CD key to do this, so you still wouldn't be able to "borrow" someone else's CD and Product Key. But still, if you've already got the key, and you're just missing the installation CD, this method will suffice for reinstalling Windows. Going even further, you could copy the i386 folder to a CD, along with any other tools you might use when building and customizing a Windows XP installation.
